Graduation and the Road Ahead, Behind, Sideways...

Many months have passed since my last blog entry. I apologize for that. My last semester at MIT was an enjoyable one. I got to take Victor Guillemin's course, 18.952 - Theory of Differential Forms, with a friend of mine and I always love chatting about courses with people.

I have put together a Googlepages page summarizing my academic work and projects from the past four years. It can be accessed here:

Justin M. Curry - The Collected Works of a Philosopher-Mathematician

I know it sounds depressing, but I, along with many of those graduating in 2008, have really struggled with "letting go" and leaving my undergraduate career behind and entering the "real world." Granted the real world for the next 5 years will be graduate school at the University of Pennsylvania, working with any of the fine mathematicians there, but still, the idyllic times of college have come to an end. You can see my proof of purchase below:





Sasha and I had a wonderful time decorating our mortarboards - a quirky re-capturing of an otherwise boring ceremony - making it an individualized expression of coming to terms with our frenetic time at MIT. I discovered that one of the best ways to make a three-dimensional "8" is to first make a mobius strip and then pinch the middle together. From the photo you can see that Sasha has spelled "MIT" using Feynman Diagrams and I have contented myself with a knockoff of one of the many variants on the MIT logo.

How did I get here from my last blog post on January 20, 2008? Over 5 months have passed and no letter to my internet home? What gives? I will hope to answer some of these questions in the next couple of posts. Most of these recent posts were written around the end of June and the beginning of July, but I have altered the dates to present them in a given order. This post I'm dating June 6th, 2008 to reflect my graduation date. The one below I've dated April 15th to symbolize the common notification deadline for graduate schools in the U.S. I hope you enjoy my re-telling of these stories!

Quantum Mechanics and Experience

One of the classes I'll be taking this semester is 24.111 - Philosophy of Quantum Mechanics. Today I just bought the required text, Quantum Mechanics and Experience by David Z. Albert. The book looks pretty good, with a solid layman introduction to the foundational principles of quantum mechanics.

My dance with Quantum Mechanics (QM) has been a really interesting one. Prior to my coursework this past year at Cambridge, I objected to the conclusions of quantum mechanics advertised in popular science books because it ran against my mental model of the universe. My struggles with the conceptual foundations of QM were very much in the same vein as Einstein's critique of the theory. The idea that probability has a real existent status deeply troubled me. Always before, probability was a description of averages and distributions. A coin toss -- the idol of probability -- was still fundamentally governed by Newton's Laws, the forces in the room, the initial configuration of the coin in your hand, the torque, the impulse of your thumb on the coin, the chaotic turbulence of the air molecules in the room, the list goes on but all the initial configurations and momenta could theoretically be specified and then the entire motion could be simulated as the solution of a large system of nonlinear ordinary differential equations (ODEs) -- Laplace's Demon all over again. But QM is a whole different bag of nuts... Instead of solving specifically for things like position and momentum and energy, you have state vectors, and your eigenfunctions of these operators form the basis of an infinite-dimensional space known as Hilbert space. What's new about all of this is that our description of a particle is described by the time evolution of the coefficients of each of these eigenfunctions. Now we can't perceive this superposition, but rather -- and this is the really crazy bit of the whole theory -- only the eigenfunctions can be measured. So our particle is like a point wandering around in infinite dimensional Hilbert space when no one is looking. It's like Mr. Observer finally shines his flashlight in the car window and asks "Hey!?! What are you kids doing?!?" and our couple is always caught in any one of these (usually an infinite number of) compromising positions, but they're never caught scrambling to put clothes on or in a acrobatic transition or superposition of pages of the Kama Quantum Sutra.

So it will be interesting to see what insights 24.111 will bring, and complemented with 18.102 - Introduction to Functional Analysis, this should be a tantalizing semester spent exploring Hilbert space!